HKAL Extra Exercise : Part 4 Electricity and Electromagnetism
Chapter 14 Capacitance
14.1Capacitance
1.A potential difference V is applied between two large parallel plates, distance s apart. An electron, mass m, charge –e, starts from rest at the negative plate and travels across the gap to the positive plate. Its final speed is
A..B..C..D..
2.
The figure above shows a charged parallel plate capacitor. P is a point between the plates and its distance from plate A is x. If V is the electric potential at point P, which of the following graphs best represents the variation of V with x? (The separation of the plates is s.)
A.B.C.D.
Capacitance of Two parallel Plates
3.A parallel-plate capacitor is formed by two circular metal plates. To determine the capacitance C, a student measures the radiusr and separation d of the plates.
If the maximum percentage error of r = 7%,
the maximum percentage error of d = 3%,
then the maximum percentage error for C will be
A.7%B.10%C.13%D.17%
4.If the length of the sides of the square plates of a parallel-plate capacitor is decreased by 25%, its capacitance will
A.decrease by 25%.B.decrease by 56%.
C.increase by 33%.D.increase by 33%.
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HKAL Extra Exercise Chapter 14 Capacitance
5.
In the capacitor arrangement shown in the diagram, plate P has been charged and connected to the electroscope. If plate Q is moved upward from plate P, the gold-leaf will
A.remain where it is.
B.diverge a lot more.
C.diverge a little more.
D.fall slightly.
6.
A parallel-plate capacitor is first charged by connecting it to a battery. After disconnecting the battery, one of the plates of the capacitor is shifted toward the other plate as shown. What would happen to each of the following quantities ?
V : the potential difference between the plates
Q : the magnitude of the charge on each plate
C : the capacitance of the capacitor
V QC
A.increased unchanged increased
B.unchanged decreased decreased
C.decreased decreased decreased
D.decreased unchanged increased
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HKAL Extra Exercise Chapter 14 Capacitance
Capacitors with Dielectric
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HKAL Extra Exercise Chapter 14 Capacitance
7.C1 and C2 are plane parallel plate capacitors of the same area. The plates of C1 and C2 are separated by slabs of the same dielectric material of thickness d and 5d respectively. The capacitance of C1 is 0.24μF. The capacitance of C1 and C2 connected together in series is
A.0.04μF.B.0.05μF.
C.0.20μF.D.0.29μF.
8.
A sheet of dielectric occupies part of the space between the parallel of an evacuated capacitor. P is a point in the dielectric and Q is a point in the vacuum between the plates. Neglecting edge effects, the electric field strength at Q when the capacitor is charged is
A.the same as that at P.
B.equal in magnitude but opposite in direction to that at P.
C.less than that at P.
D.greater than that at P.
9.
Two large metal plates A, B are oppositely charged and placed a small distance apart. A piece of metal M is placed centrally between the plates. Which of the following graphs shows the variation of electric potential V from A to B ?
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HKAL Extra Exercise Chapter 14 Capacitance
A.B.C.D.
14.2Combination of capacitors : Equivalent Capacitance
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HKAL Extra Exercise Chapter 14 Capacitance
10.A parallel-plate capacitor of capacitance C0 is formed by two rectangular metal plates having separation d. Now each of the plates is cut into five smaller, identical ones to form two capacitors, each with plate separation 5d. What is the capacitance when they are connected in parallel ?
A.(1/50)C0B.(2/25)C0
C.(1/10)C0D.(2/5)C0
11.Which one of the following combinations has the greatest capacitance?
A.
B.
C.
D.
12.
Three identical capacitors, each of capacitance C, form a network as shown. What is the equivalent capacitance between terminals X and Y ?
A.B.
C.CD.3C
13.
Circuit A Circuit B
Three identical capacitors are connected to the same d.c. source in series (circuit A) and then in parallel (circuit B). The magnitude of the ratio of the total charges stored by the capacitors in circuit A to circuit B is
A.9.
B.3.
C.1/3.
D.1/9.
14.
In the above circuit, two charged capacitors C1 and C2 are connected across AB so that it is parallel with an initially uncharged capacitor C3. Which of the following statements is/are correct when switch S is closed ?
(1)The quantity of charge on C1 is the same as that on C3.
(2)The combined capacitance across AB will increase.
(3)The potential difference across AB will increase.
A.(2) only
B.(3) only
C.(1) and (2) only
E.(1), (2) and (3)
15.
Three capacitors are connected to a 70 V supply as shown in the above circuit. The voltage at the output is
A.10 V.
B.28 V.
C.42 V.
D.60 V.
16.
A voltage of 1000 V is applied across AB in the capacitor network shown above. The voltage across CD is found to be 450 V. If after some time, the voltage across CD suddenly jumps to 0 V, which capacitor(s) has been shorted ?
A.1μFB.2μF
C.4μF
D.All 4 capacitors have been shorted.
17.
A charged capacitor C1 is connected to an uncharged capacitor C2 as shown. If
E1 = the total energy stored in C1 and C2 before connection, and
E2 = the total energy stored in C1 and C2 after connection,
Which of the following is/are correct?
(1)The charges discharged by C1 is equal to the charges charged in C2.
(2)After connection, the charges stored in C1 is equal to that in C2.
(3)After connection, the p.d. across C1 and C2 are in the ratio
.
A.(1) onlyB.(3) only
C.(1) and (2) only
D.(2) and (3) only
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HKAL Extra Exercise Chapter 14 Capacitance
14.3Energy Stored in a Capacitor
18.The energy of a 9μF capacitor when having a stored charge Q is E. The energy of a 3μF when having a stored charge 2 Q is
A.4/3 E.B.2 E.C.4 E.D.12 E.
19.The two plates of a parallel-plate capacitor initially carry equal amounts of positive charge. If some charges are transferred from one plate to another, the charges on the plates are respectively -300μC and -700μC. The potential difference across the plates becomes 80 V. What is the capacitance of the capacitor ?
A.2.5μFB.3.8μFC.8.8μFD.12.5μF
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HKAL Extra Exercise Chapter 14 Capacitance
Charging a Capacitor with a Cell
20.
A parallel-plate capacitor is connected to a battery as shown. What will happen if the separation of the plates is decreased?
capacitancevoltagecharge
A.increasesdecreasesincreases
B.increasesunchangedincreases
C.decreasesdecreasesincreases
D.increasesunchangeddecreases
21.
In the above circuit, the battery has an e.m.f. of 9.0 V and all the capacitors are identical. Initially none of the capacitors are charged. The switch is first connected to X and then to Y. What is the final potential difference between Z and Y ?
A.1.0 VB.1.5 V
C.3.0 VD.9.0 V
Moving Apart Two Charged Plates
22.A parallel-plate capacitor is charged by a battery and the energy stored in the capacitor is E. The circuit is still connected to the battery. If one of the plates is moved so that the plate-separation is halved, the electrical energy stored in the capacitor will
A.decrease to E/4.
Bremain the same.
Cincrease to 2E.
Dincrease to 4E.
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HKAL Extra Exercise Chapter 14 Capacitance
23.A parallel-plate capacitor is charged by a constant voltage source. With the plates disconnected from the source, the plate separation, d, is then gradually increased from an initial value d0. Which of the following graphs best shows the relationship between the energy, U, stored in the capacitor and plate separation, d ?
A.B.C.D.
14.4Charging and Discharging
24.A capacitor has a capacitance of 1 farad. Which of the following deductions must be correct ?
(1)It gains 1 joule of electrical energy when it has 1 coulomb of charge.
(2)It stores 1 coulomb of charge at a potential difference of 1 volt.
(3)It will be fully discharged in 1 second by a constant current of 1 ampere.
A.(1) onlyB.(2) onlyC.(1) and (2) onlyD.(2) and (3) only
Charging a Capacitor At a Constant Rate
25.A capacitor is charged by a constant current. Which of the following graphs shows the time variation of the charge stored in the capacitor during the charging process ?
A. B.C. D.
Charging a capacitor via a resistor
26.
A capacitor and a resistor are connected in series to a d.c. voltage supply as shown. At time t = 0, the key K is closed. Which of the following statements is/are true?
(1)The final charge on the capacitor does not depend on the resistance of R in the circuit.
(2)The capacitor is almost fully charged after a time t = CR.
(3)At any time t the potential differences across R is a constant.
A.(1) only
B.(3) only
C.(1) and (2) only
D.(2) and (3) only
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HKAL Extra Exercise Chapter 14 Capacitance
27.
A changing voltage V is applied across AB in the circuit shown. The potential difference VAC across the capacitor is found to vary with time t as shown. Which of the following graphs shows the variation of potential difference VR across the resistor R with time t ?
A.B.
C.D.
28.
An initially uncharged capacitor of capacitance C is connected in series with a resistor R and a battery of e.m.f. E. What will be (1) the energy dissipated by R in fully charging up C and (2) the total work done by the battery in fully charging up C?
Work done byEnergy stored
battery in C
A.CE2 0
B.CE2 0
C.C E2 C E2
D.CE2 C E2
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HKAL Extra Exercise Chapter 14 Capacitance
Time constant
29.A 4μF capacitor is discharged through a resistor R. If the time constant of the discharging circuit is 5 ms, what is the resistance of the resistor ?
A.20 kΩB.2 kΩC.1.3 kΩD.0.8 kΩ
Discharging a capacitor via a resistor
30.A capacitor is charged to a p.d. of 150 V and then connected across a resistor. After 1 s, the p.d. across the capacitor is 100 V. The time constant of the circuit is
A.0.22 s.B.0.41 s.C.2.47 s.D.5 s.
31.
A charged capacitor C, of 15μF capacitance, is connected in the circuit above. For a period of 20 s, the current is kept constant at 30μA by continuous adjustment of R. During this period, the p.d. across the capacitor has fallen by
A.40 V.B.7 V.C.2 V.D.0.6mV.
32.A 4μF capacitor, which is initially charged, is discharged through a 25 Ωresistor. The initial charge on the capacitor is 4 ×10-3 C. What is the maximum current during discharge ?
A.400 AB.100 AC.40 AD.0.1 A
33.A charged capacitor is connected across a resistor. Its voltage drops to one-fifth of the original value in 20 s. Find the time constant of the circuit.
A.100 sB.32.2 sC.15.0 sD.12.4 s
34.A charged capacitor is connected to a voltmeter with resistance 1 MΩ. The voltmeter reading drops from 8 V to 6 V in 11.2 s. Find the of capacitance of the capacitor.
A.39μF.B.20μF.C.6.3μF.D.5.4μF.
35.
A capacitor C is charged to a certain p.d. and then discharged through a resistor R. The variation of the current i with time t is shown in the above graph. Which of the following is/are correct ?
(1)The time constant of the circuit is about 3.6 s.
(2)The area under the graph is proportional to the square root of the charge stored in the capacitor.
(3)If the resistance of R is halved, the current at t = 0 will also be halved.
A.(1) onlyB.(3) onlyC.(1) and (2) onlyD.(2) and (3) only
36.A ‘jumbo’ capacitor has capacitance 500 000μF. Such a capacitor charged to 25 V would
(1)provide a mean current of 1 mA for 12500 s.
(2)be completely discharged through a 0.2 Ωresistor in 1 s.
(3)store 156 J of electrostatic energy.
A.(1) onlyB.(3) onlyC.(1) and (2) onlyD.(2) and (3) only
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HKAL Extra Exercise Chapter 14 Capacitance
37.
In the circuit shown, S is connected to P until the capacitor is fully charged. Then S is switched to Q. What is the initial value of the current through the 8 MΩresistor ?
A.1.6 ×10-6 A B. 3.0 ×10-6 A
C.6.3 ×10-6 A D. 4.0 ×10-4 A
38.In a circuit with a vibrating reed switch, a 7μF capacitor is charged from a battery of e.m.f. 5 V and completely discharged through a resistor with a frequency of 20 Hz. The average power dissipated as heat in the resistor is
A.25μW.B.35μW.
C.600μW.D.1.8 mW.
39.
Using the vibrating reed switch S, in the above circuit, the capacitor C is charged from battery B and completely discharged through the resistor R with a frequency of 30 Hz. When a CRO is connected across C, the wave form will look like :
A. B.
C. D.
40.
In the above circuit, a capacitor C is charged from a battery E and then completely discharged through a resistor R using a vibrating reed switch S. The waveform displayed on the screen of the CRO with suitable time base should be
A. B.
C. D.
41.
(a) (b)
A square wave voltage VS, as shown in Figure (a), is applied to a circuit containing a 1 mF capacitor and a 4Ωresistor connected in series. Which of the following graphs best represents the variation of the p.d. V across the resistor with time t ?
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HKAL Extra Exercise Chapter 14 Capacitance
A.B.C.D.
42.
A charged capacitor C1 , is connected to an uncharged capacitor C2 of smallr capacitance through a resistor R as shown above. When switch S is closed, which of the following statements is correct ?
A.The total charges on the two capacitors falls.
B.The final charge on C2 is greater than that on C1 .
C.The total energy stored in the capacitors falls.
D.The potential difference across C1 falls.
KEY :1 – 10 : BDDBC, DADAB,11 – 20 : CADAB, DADAB,
21 – 30 : BCABD, ADCCC,31 – 40 : ACDAA, CCDCB,
41 – 42 : CB.
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HKAL Extra Exercise Chapter 14 Capacitance